Shape coexistence and three-quasiparticle excitations in 123, 125I

Nuclear Physics A485 (1988) 31-45 North-Holland, Amsterdam

SHAPE COEXISTENCE AND THREE-QUASIPARTICLE EXCITATIONS

IN

123'12Sl

L G KOSTOVA, W ANDREJTSCHEFF and L K KOSTOV

Bulgarian A~adem3 oJ Soences, lnstttute for Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgarm F DONAU, L KAUBLER, H PRADE and H ROTTER

Akademle der Wzssenschaften der DDR, ZentrahnsntutJur Kernforschung Roswndorf 8051 Dresden, GDR Recewed 4 January 1988 (Rewsed 21 March 1988~

Abstract: Applying the generahzed centrold-shlft method new half-hves were measured for the following ~23 ~-~51levels excited in (a, 2n) reachons T1/2= 0 8 ± 0 1 ns ( Ele ~ = 302 2 keV), 0 2 ± 0 1 ns (641 3 keV), 0 2 + 0 1 ns (943 5 keV) and 0 4 ± 0 1 n s ( 2 0 0 0 7 keV) m 1231, 0 2 ± 0 1 ns (935 8 keV), 1 6 ± 0 3 ns (2350 6 keV) and 0 3 ±0 1 ns (2791 0 keV) m ~-~51 Further, the known half-hves of the levels at 178 0 keV m 123I and 188 4 keV m ~-'si have been confirmed The hfetlmes of the 9+ intruder states m ~3 t:51 are compared to calculattons wHhm the core-quas~partlcle coupling model Indications for 3QP configurations m ~251 are found NUCLEAR REACTIONS t21 i.~Sb(a ' 2n), E =27 MeV, measured Ev, I~, c~y(t) 123 12~ 1 deduced levels T~/~, B(A ) Enriched targets, Ge detectors Generahzed centrold-shlft analysis, core-quaslpartlcle couphng model calculations

1. Introduction O n e o f t h e m o s t i n t e r e s t i n g f i n d i n g s i n t h e o d d - A n u c l e i a b o v e t h e Z = 50 c l o s e d s h e l l is t h e c o e x i s t e n c e o f e x c i t e d s t a t e s w i t h d i f f e r e n t s h a p e s [ c f e g r e f 1) a n d references therein]

Collective band

s t r u c t u r e s b a s e d o n p r o l a t e g9/2 p r o t o n - h o l e

c o n f i g u r a t i o n s as w e l l as o n o b l a t e d5/2, g7/2 a n d hi1/2 p r o t o n - p a r h c l e been identified in the odd-A have been measured

orbitals have

i o d i n e i s o t o p e s 1-5) T h e r e b y , n a n o s e c o n d

lifetimes

f o r t h e i n t r u d e r 9+ s t a t e s i n 117-~21I

The structure of the nuclei in this mass region has been considered within different theoretical approaches (CQPC)

( c f ref. ~)) O n e o f t h e m is t h e c o r e - q u a s l p a r t l c l e

coupling

m o d e l , w h i c h w a s s u c c e s s f u l l y a p p l i e d to ~2~I [ r e f 6)] A h a l f - l i f e o f 0 4 n s

w a s t h e r e b y p r e d i c t e d f o r t h e 9+ b a n d h e a d in t h i s n u c l e u s was to test this prediction

One aim of this work

a n d t o e x t e n d t h e s y s t e m a t l c s o f t h e 9+ i s o m e r s t o t h e

i o d i n e i s o t o p e s w i t h A = 123 a n d 125 0375-9474/88/$03 50 O Elsewer Science Pubhshers B V (North-Holland Phystcs Pubhshmg Dl~tslon)

32

L G Kostova et a l / Shape coertstence

The locahzation of high-lying isomers can be helpful m the idenUficatlon of three-quasiparticle configurations 5,7) This was another motivation for our isomer investigations. Prehmmary results from the present study were reported in ref. s)

2. Experimental techniques and analyzing procedure Using the 27 MeV t~-partlcle beam of the Rossendorf cyclotron, excited states of

123"1251 were populated via the 121'123Sb(ot, 2n) reactions, respecUvely. The targets consisted of 5b204 of about 20 m g / c m 2 thickness enriched an 121Sb to 98 5% and m 1235b to 98%, respectively. The t~mmg measurements were performed by means of the delayed 3'-rf. method 9) The start signals for the Ume-to-amphtude converter (TAC) were supphed by a 10 cm 3 planar Ge(Li) detector The stop signals for the TAC were derived from the cyclotron oscillator. The energy resolution was 2 0 keV at Ev ~-200 keV The time resolution of the experimental set-up was 2o-0= 6 ns for Ev > 300 keV. Two independent measurements have been performed for each nucleus. Thereby, 96 tame distributions (corresponding to 96 selected windows in the G e ( L 0 energy spectrum) were recorded in a 96 × 128 channel matrix The measured Ume spectra were analyzed according to the generalized centrold-shift method, which is described in detail in refs 9.1o) By this method, the contributions from the Compton background and the random coincidences to the net time distribution of each peak of interest are properly accounted for The centroad diagram is constituted by the centrolds of the time distributions (time centrolds) plotted versus y-ray energy The lifetimes to be measured are related to the centrold-shffts from the zero-t~me line This hne connects the time centrolds of prompt transmons F*g. 1 shows parts of the measured 3,-ray spectra with the (time) windows on peak and Compton background posmons indicated Some examples of prompt and delayed ume dastrlbutions obtained m both reacUons are displayed an fig 2.

3. Experimental results 3 1 THE NUCLEUS 123I The centroid diagram obtained in the 121Sb(a, 2n)123I reacUon is displayed in fig. 3. In this nucleus 2.4), a relatively long-hvmg state (TI/2 = 28 ns) has been found at 2660 0 keV (fig 4) This isomer feeds the members of the rotational band built on the 9+ level at 641 3 keV which to some extent makes difficult the determination of the half-life of the 9+ level at 641 3 keV Although the procedure which accounts for random coincidences an a time distribution ehmmates a substantial part of the taft arising from delayed feeding, the time centroids of all cascade transmons above the 9+ level are shafted up to 0 4 ns with respect to the zero-time hne (cf figs. 3 and 4) due to the delayed feeding However, the measured devmtions from the zero-tame

104

2

105

2

"-

i

& I L IIII

I ~

500

I

1H I

'~.,t

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I

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Z

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I

.,,.. I

o

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t/') c,4

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l

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~

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,

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I.

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II, ,, ~ I

r

~

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,

II fl

÷ ~.

I

i

I

i

• [I

i

~

r

I

,,I I it

i

CHANNEL NUMBER

1000

I_~ ~

o0

"--.

CD

121Sb + 27 MeV 4He

i

i

i

rt~4 . co L,3

I

I

-4~ ~

i

,

,

i

,

i

,

l

~

1500

I

I

a

I

t"O O0 o~ ~ U~ t"-0-4"

,

~ t-..

I

~1

J

~ FULL ENERGY PEAK

~o ~ ~ ~o'° ~o -4" t.t)

I

WINDOWS '

i

I

I COMPTON BACKGROUND

TIME

Ge(LI), PLANAR, lOcm 3

]

,

IHI

i

2000

I

--

(a)

Fig 1 Gamma-ray spectra representing parts of the energy axis of the full e n e r g y x time matrices recorded m the reactions investigated The full TAC region employed here was about 80 ns (the repetition period between two beam bursts is about 90 ns) The positions of the (time) windows selected m the energy spectra are marked (a) The reaction 121Sb+27 MeV a The y-ray trans~tlons belonging to 12~I are labelled by their energies m keV *The origin of the 258 0 keV y-ray transition is not identified Its time centrold is lying on the zero-time hne (cf figs 2a and 3)

0 t_)

:D

z

I'--

LD

5.105

I

0 0

z

U3 I--

2 10 4

5

1o5

2

5x105

I

¢<'J ~
I

,

0# z

I

.-.~,,,

~ ~o

T

i

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l

i

i

I

+"~"+'

I

I

,

I

~ t ~ ,'

1

I

I

o~

+

1000

' ~~',

~I

~, o

,o

c:) co M

1235b

I

I

'

~.

I

-4-

CHANNEL

I

~~

"--*

27 MeV

p tl

I

~

I

~

I (:~Lr> o')

,

I

,

~ IJD

l

1500

i

I

^

t-.t-~

i

q

I

:-Z ~co co

I

,

WINDOWS:

I

I:i',

P"

I <"+

~

2000

I

+

H HI

I I

•~ ..__

,

('Y)

+~T."

.,4"

I

I@ I

,

+'

¢'+J

,

m

,

£:o

(b)

I

+"""~

I COMPTON BACKGROUND la FULL ENERGY PEAK

TIME

Ge(L,), P L A N A R , 10 cm 3

, # - ~ , ~,'r':'----~....~ L

~

' .+,V'L.. "

~

, + r--+'+-+

~

NUMBER

i

u-) i

~--,L

, ~u

Z'He

l , l , l i l i l , l , l , l + l l l , l i l ' l i l + l

Fig lb The reaction '~-3Sb+27 MeV a The "/-ray transitions belonging to ~ 1 are labelled by their energies in keY Cf caption to fig 1

500

al

~1~ c o~l a

u_

I

+=

r~

r~

t"

35

L O Kostova et al / Shape coex:stence I I

I

[

I

I

I

l

121Sb + 27MeV 4He

106

I

oA E~=6413keV oB Eir=6558keV

oe~.

~°

oo

i

IT

o

o

~o

AIIB

104

5

°°I

o

o o

CENTROIOS

o.~ o

o

o

102

103

0 B6ns/CHANNEL 65

°0

o

~ oO

°ooe I

o

810~

°o

CENTROIDS

I

oo

o

o

O

0

; °o

(

(b)

START Oe(Ld, PLANAR,10cm 5 STOP CYCLOTRON R.F

o

"

I

~'...

STOP CYCLOTRONRF 10 4

105

I

NET TIME DISTRIBUTIONS

START Ge (LI), PLANAR,10em

oOOo

I

121Sb ÷27MeV 4He

(a)

NET TIME DISTRIBUTIONS o A E~,=2725keV * B Eg--2580keV

I

I

I

I

I

70 75 60 85 90 CHANNEL NUMBER

086ns/CHANNEL 1

I

95

70

I

I

I

I

75 80 85 90 CHANNEL NUMBER

I

95

Fig 2 The net time distributions obtained after subtracting Compton contnbuuons and random comodences for some y-ray transitions With full dots are shown time curves with centrolds lying on the zero-time line, 1 e prompt, while the open circles represent delayed time distributions With arrows are marked the centrold posmons of the corresponding time dlstnbuUons All net time distributions have been uniformly analyzed within limits chosen at those ADC channel numbers on both sides of the corresponding (time d~strlbutton) peak where the accumulated counts decrease down to 10% of the peak value (a) Net time distributions obtained in the reaction t-'tSb+27 MeV c~ (cf figs la and 3) (b) Net time distributions obtained m the reaction 12tSb+27 MeV t~ (cf figs la and 3) h n e o f t h e t i m e c e n t r o l d s o f t h e 503 0 a n d 641.3 k e V t r a n s m o n s d e - e x c i t i n g t h e 9+ l e v e l at 641.3 k e V a r e c l e a r l y l a r g e r t h a n t h o s e o f t h e c a s c a d e t r a n s i t i o n s (fig 4) T h i s is a n e v i d e n c e t h a t t h e l a t t e r state has a m e a s u r a b l e h f e t t m e A f t e r c o r r e c t i o n for the delayed feeding we derived T1/~(641 3 keY) = 0 2 + 0 . 1 ns 9+

for the ~ level T h e ~ - state at 943.5 k e V d e c a y s by t h e 272.5 a n d 391 2 k e V t r a n s m o n s (fig. 4) T h e t i m e c e n t r o l d s o f b o t h t r a n s m o n s i n d i c a t e a n i s o m e r i c c h a r a c t e r o f t h e 11- level. U n f o r t u n a t e l y , t h e 391 2 k e V t r a n s i t i o n is u n r e s o l v e d f r o m t h e 391 8 k e V o n e , w h i c h d e - e x c i t e s t h e 4 + state at 2082 2 k e V O n t h e o t h e r h a n d , t h e r e are n o i n d i c a t i o n s f o r a n y d e l a y c o m p o n e n t m t h e d e c a y o f t h e 2082 2 k e V l e v e l T h e r e f o r e , it c a n b e a s s u m e d t h a t t h e c e n t r o l d - s h i f t o b s e r v e d f o r t h e t i m e d i s t r i b u t i o n c o r r e s p o n d i n g to t h e 391 k e V g a t e m t h e y - r a y s p e c t r u m is m e r e l y d u e to a c o n t r i b u t i o n f r o m t h e

36

L G Kostova et al / Shape coexistence I

I

123Sb NET

i

+

I

i

27MeV

i

Z'He

I

(c)

TIME DISTRIBUTIONS

10 4

START Ge(LI),PLANAR,10Cm3 "

)A E~-= 7961keY ) B E~'= 7983keY

STOP CYCLOFRON RF

o0oo0

o 6 °°° ° *! 103

o°

oo * t

o °{°

•

o °

00 °

o

A

°102

O0

o

t

B

t

~ |

° I

CENTROIDS

oo o

0 86ns/CHANNEL

10 I

60

I

1

I

1

I

65 70 75 80 85 CHANNEL NUMBER

I) 9O

Fig 2c Net t,me distributions obtained m the reactmn t2sSb+27 MeV a (cf figs lb and 5) Cf caption to fig 2 391 2 keV t r a n s i t i o n In the q u a n t i t a t i v e a n a l y s i s we have u s e d the t i m e d i s t r i b u t i o n o f the 272 5 keV t r a n s i t i o n a n d d e r i v e d a h a l f - h f e o f T,/2(943 5 keV) = 0 2 + 0 1 ns for the ~ - state H a g e m a n n et al. 2) h a v e t e n t a t i v e l y p r o p o s e d two levels at 302.2 a n d 2000.7 keV d e - e x c i t e d b y the 302.2 a n d 310.2 keV t r a n s m o n s , r e s p e c t i v e l y (fig. 4). T h e time c e n t r o i d s o f these t r a n s i t i o n s c l e a r l y d e v i a t e f r o m the z e r o - t i m e hne (fig. 3) revealing the half-lives o f T1/2(302 2 keV) = 0.8 + 0 1 ns and 7",/2(2000.7 keV) = 0.4 + 0.1 n s . T h e level at 178.0 keV d e c a y s to the g r o u n d state T h e half-life T t / 2 (178 0 keV) = 0.3 +0.1 ns as m e a s u r e d in this w o r k agrees s a t i s f a c t o r i l y with the a l r e a d y k n o w n v a l u e 7"]/2=0 3 6 + 0 . 0 2 ns, ref. '~).

L G Kostova et al / Shape coexistence I

I

I

I

37

I

I

121Sb (~x,2n)123I d UJ z z < I (_9

CENTROID POSITIONS OF TIME DISTRIBUTIONS o WITH INTERPOLATED BACKGROUND • OF INTERPOLATED BACKGROUND

z83

SUBTRACTED

e,J

o

___82 °81

o

a

~80

~

o

g

N N

"4

I-(J

0 86ns/CHANNEL

78 I

I

I

I

I

I

I

200

300

400

500

600

700

800

GAMMA -RAY ENERGY [MeV]

Fig 3 Centrold diagram obtained from the reaction ]2]Sb(a, 2n)~2Sl m the 3,-energy region 200-850 keV Open circles represent time centrolds labelled w . h the t r a n s m o n energy m keV Full circles represent centrmds o f U m e d l s t n b u t m n s contributed by the C o m p t o n background The radn of the c~rcles correspond to the statlsUcal errors The sohd curve indicates the zero-t~me hne

28ns (2112") 26600 I (2_48_1_7~ 2961 / (19/2") t 23619 399 5 671 '5 1 1 + 345 6

.... 19/2(13/2-)

"~-~'-

2039 9 I 17/2" 5868

I 14531

12ooo~ 18717 I

1 5096

272 5

9/2"

671 o 532 ?

\

7/2 }20822/(17/2~) t 20163

--~--

i

310 2

391 6

//

I /.13 7

16766\IS12+ t169od/ , /1161~, It 16o~6

37'~6 ?o,o? /

11565

~1 2 60/*I

9•2* ~ ]

,6/2" I

1~12+

7152

/ 1312" I / 1-0--2-n'~'1'\11/2- 1 943 5 689 0

-

13/2 I 13166t 630 0 674'3 / /

762 5 11/2+

79/.1

~62/*

133i2 9/2+t { 6/.13

/

I/.1~0

s62/*11t

7/2" t

'~/*/

I

( ~

123

53170

Fig 4 ParUal level scheme of 1231 according to refs 2 4) and the present work The boxed half-hves were measured m these investigations

L G Kostova et al / Shape coext~tence

38 32

THE

NUCLEUS

225I

The centroid positions o f most time &stributlons measured m the 123Sb(a, 2n)a25I reaction are displayed versus the y-ray energy in fig 5 The dewation o f the time centro~d from the zero-t~me hne obtained for the 822.2 keV transmon results in a half-hfe o f T~/2(935.8 keV) = 0 2 + 0 . 1 ns for the 9+ state de-excited by this transition (fig 6). An important result o f this work is the observation o f two high-lying isomers at 2791 0 and 2350 6 keV, respectwely The 2791.0 keV level is fed by the prompt 308 0 keV transmon (figs 5 and 6) and decays w a that o f 204 3 keV Evaluating the centrold-shlft observed for the 204 3 keV transition we determine T,/2(2791 0 keV) = 0.3 + 0 1 ns The level at 2350.6 keV is depopulated by transitions o f 686.0 and 796.1 keV (fig 6) The time centroids obtamed for both transitions are unambiguously shifted from the zero-t~me hne (fig. 5). The reason for the smaller deviation observed for the time centro~d o f the 686.0 keV transition is the influence o f the more intense and prompt 684 1 keV transition Taking into account also the delayed feeding from

I

I

I

I

I

I

I

123Sb{cx,2n1125T CENTROID POSITIONS OF TIME DISTRIBUTIONS J w

0 WITH INTERPOLATED BACKGROUND SUBTRACTED • OF INTERPOLATED BACKGROUND

z

Z

to

u~

~

to

z81

r.-.

N

to

cn

o

~

•

o Go

~

•

o ~r

c~79 I

O

E78

•

o

o

i:o-~ ~

e.l

-o

Z

c~77

~J

0 86ns/CHANNEL

I

I

200

300

C~ N

1

I

I

I

I

400

500

600

700

800

GAMMA- RAY ENERGY[MeV]

Fig 5 C e n t r o l d p o s l U o n s o f y - r a y t i m e & s t n b u t ] o n s as o b t a i n e d m the reaction b e t w e e n 180 a n d 770 k e V ( c f e x p l a n a t i o n s to fig 3)

--

1235b(ot, 2n)1251 f o r Ez,

39

L G K o s t o v a et al / Shape coextstence

{23/2 ±) 30990 I 3O80 (21/2±) ~ 2791 0

(21/2÷)

÷,20/.3 119/2-1 [ 2~667

2737

8

236 1

1912-

I

22?8 2 ( 1 7 / ? ' ~k~0 6 1 - - ~ ~

613 6

686 0

850 2

7961 "~15/2 ÷

155/. 5

6841

15/2*

I

1997 3

380 6 13/2" I 16167 /

3/*6 8 13/2+ I 12037 11/2÷ t 12699 3341 / 9/2 6061 / ÷ ] 935 8 822 2 /

579 7

786

3806 /*89 3 9/2÷ I 70/*3 ~

/

i

654 5

70l. 3 5/2' I

18878

17/2"

06ns

712 ÷

t

1136

59i6/3/2.

1

188~ F6-~q 0

125T 53 "72 Fig 6 ParUal level scheme of JzsI according to refs z 4) and the present work The boxed half-hves were measured m these mvestlgaUons

the 2791 0 keV level w e derived a half-life

T~/2(2350.6 keY) = 1 . 6 + 0 3 ns The shifts o f the time centrolds observed for the 236 1 , 3 8 0 . 6 , 579 7, 654 5, 704 3 and 786 4 keV transitions are associated with delayed feeding from the 2791 0 and 2350.6 k e V levels Therefore, only an upper hmlt can be given for the half-lives o f the 1] and (19±) states T~/2(1084 9, 2586 7 keV) < 0 . 2 ns The half-hfe o f the 3+ level at 1 8 8 . 4 k e V was k n o w n to be T t / ~ = 0 3 4 + 0 . 0 2 n s ref ~ ) Our result 7"1/2(188.4 keV) = 0 2 + 0 1 ns is s o m e w h a t lower but generally not in contradlctton to this value

4. Discussion

41 GENERAL REMARKS The absolute e l e c t r o m a g n e t i c transition probabilities as d e t e r m i n e d from the m e a s u r e m e n t s m this w o r k are s u m m a r i z e d in table 1. In subsect 4.2 w e discuss the data relevant to the core-quaslpartlcle-coupling m o d e l . The e v i d e n c e for the three-quaslpartlcle states m ~25I ts presented m subsect 4 3

40

L G Kostova et al / Shape coexistence

TABLE 1 Electromagnetic transmon rates determined m the present studies for ~231251

El¢,,(keV)

T~/2¢~p(ns)

J~-)

JT)

E.r(keV)

o'L

B(o'L) (W u )

5030 641 3 272 5 391 2

M1 E2 E1 E1

(41±20)×10 4 0 37±0 18 (5 6±2 8) x 10-5 (3 3 + 1 6) x 1 0 - 6

822 2 380 6 489 3 6860 796 1 236 1 2043

M1 E1 E1 MI* El* M1 M1

1231

6413

02±01

9+ ~

943 5

0 2±0 1

L1-2

7+ ~ ~+ _9+2 9+

1251

935 8 1084 9

0 2+0 1 <~0 2

9+ L~2

7+ 9+ 2 9+

23506

1 6-,-03

.L72

2586 7 2791 0

<~0 2 03+0 1

,197 .21~-

t~2 1_5+ 2 ,17~.~-

(2 0± 1 0) x 1 0 -'4 />2 3 x 10-5 i>5 5 × 1 0 - 7 (1 8±0 3)x 10-5 (1 9-,-0 4) x 1 0 - 7 1>8 3 × 10 s (79+26)x10 -s

The parmes of the states and the multlpolarmes marked with an asterisk were adopted m th~s work, while the other data are taken from ref 2) 4 2 CORE-QUASIPARTICLE COUPLING A detailed d e s c r i p t i o n o f the C Q P C m o d e l is given in ref 6) where the a p p r o a c h was successfully a p p h e d to 123I a n d a half-life o f 0 4 ns was predicted for the 9+ band head

The e x p e r i m e n t a l value m e a s u r e d in the present study (T1/2e×p =

0 . 2 ± 0 . 1 ns) is very close to the calculated o n e a n d allows i m p o r t a n t c o n c l u s i o n s a b o u t the reliability of the wave f u n c t i o n s a n d the p a r a m e t n z a t i o n of the t r a n s i t i o n b e t w e e n prolate a n d oblate shapes This g o o d a g r e e m e n t b e t w e e n theory a n d e x p e r i m e n t has m o t i v a t e d us to p e r f o r m c a l c u l a t i o n s for 125I w i t h i n the C Q P C m o d e l The results provide a further test for the v a h d l t y of the core-quasipartlcle c o u p l i n g c o n c e p t i o n . The n u c l e a r wave functions of the o d d - A n u c l e u s u n d e r study are wrttten m terms of particle-like states (particle plus 124Te core) a n d hole-like states (hole plus ~26Xe core), respectively The e q u a t i o n of m o t i o n is t h e n solved a s s u m i n g a p a i r i n g plus q u a d r u p o l e m t e r a c t l o n b e t w e e n particle (hole) a n d core The (core) q u a d r u p o l e matrix elements have b e e n c o n s t r u c t e d by m e a n s o f the a n h a r m o n i c b o s o n d e s c r i p t i o n 12) a p p l i e d to the even n e l g h b o u r s 124Te a n d 126Xe F o r the core states with R ~ = 0 +, 2~, 2 f , 4 +, 6 +, 8 +, the e x p e r i m e n t a l level energtes 11) o f ~24Te a n d 126Xe, have b e e n used The single-particle energies which d e t e r m i n e m a i n l y the relative p o s i t i o n of the b a n d heads are t a k e n from the 123I c a l c u l a t i o n s after a slight v a r i a t i o n of the h11/2 a n d g7/2 p r o t o n levels The F e r m i level A has b e e n c h o s e n to r e p r o d u c e the n u m b e r of active particles a n d is p o s i t i o n e d m b e t w e e n the g9/2 a n d d5/2 orbltals The p a i r i n g gap a n d p o l a r i z a t i o n factors have b e e n a d o p t e d also from the 1231 c a l c u l a t i o n (table 2) The c a l c u l a t e d level energtes are c o m p a r e d with the e x p e r i m e n t a l ones m fig. 7 O u r results are m good a g r e e m e n t with the e x p e r i m e n t a l findings. As in the 1231

L G Kostova et al

/ Shape coexistence

TABLE

41

2

S i n g l e - p a r t i c l e energies and polarization factors used m the present CQPC calculauon f o r 125I s p orb,tals

% (MeV)

p~

hi1/2 d3/2 st/2 g7/2 ds/2 g9/2

1 45 0 5 0 35 0 18 0 -3 4

+1 +1 -1 -1 -1 +2

The value of the p a m n g gap ~s A = 1 1 M e V and that of the F e r m i level positioned between the d~/2 and g9/2 orbltals is A = - 0 9 M e V

2.8

28

21/2"

21/2 + 1712-

19/2 +

1712÷

19/2-

>o,I2 0

zr

19/2 +

_

17/2+

13/2-

15/2 + 17/2 +

19/215/2 ÷ 17/2 +

15/2 +

15/2 +

>.(-9 tr taJ Z uJ

15/2-

15/2-

15/2 +

13/2 ÷

13/2"

15/2 + 1312 + 11/2 ÷

13/2 ÷

11/2 +

11/2-

13/2 +

11/2 +

10

9/2 ÷ -

9/2 + 11/2 + 7/2 ÷

11/2 +

11/2~

9/2 + -

9/2+ 9/2 +

9/2 +

712 +

7•2 + 5/2 +

10

11/2"

7/2 + 512 +

THEORY

125T 53--72

EXPERIMENT

F~g 7 C o m p a r i s o n o f the experimental band structures (level energies) m 125I w~th the theoretical ones calculated in the frame of the C Q P C m o d e l

case, one can reasonably describe the typical band structures built on the d5/2, g7/2, g9/2 and h~/2 single-particle states. The predicted mixing of the states is shown in table 3 The calculated M1 and E2 transition probabilities reveal that the levels can be indeed grouped in those bands as seen experimentally in the decay scheme In particular, It IS possible to reproduce the measured lifetime of the g9/2 band head with a satisfactory accuracy T~/2th----0 3 ns, which has to be compared to the experimental value T~/2e~p = 0 2 ± 0 1 ns Hence, the resulting mixing amplitudes

42

L G Kostova et al / Shape coextstence

TABLE 3 Mare components of calculated wave funcUons of states m 125I grouped to b a n d s J=

E,~ (MeV)

ds/~ b a n d fi+ 21 7+ ~2 9+ ~

0 0 489 0 626

~13+ T2

1 125 1 288

~15+ 2 17+ ~-~

1 686 1 863

~29+2 ~2+2

2 409 2 624

Wave funcUons ")

- 0 851d5/20+)+0 0 851ds/z 2+ ) - 0 - 0 631d5/22 +) - 0 - 0 121g7/~24+) 0 861d5/24 +) - 0 - 0 621d5/24+) - 0 + 0 151g7/126+) 0 861d5/~6 + ) - 0 - 0 661ds/_~6 + ) - 0 - 0 141s,/28 +) - 0 88]d~/~8+) + 0 0 761d5/28+) + 0

441d~-/'20+) + 0 17[d5/22+)-0 151ds/~z2+) 451d ~/~22+) - 0 141d5/24 +) + 0 131d5/~24+ ) 601g7/_~2+) + 0 281d5/'22+)- 0 271g7/22+)+ 0 17]g7/24 +) 421d ~/~24+ ) + 0 171d5/26 +) - 0 151d ~-/'26+) 601g7/24+) + 0 261d 5-/~24+)+ 0 251g7/~24+) - 0 211g7/26 +) 441d 5/~26+ ) + 0 16197/24 + ) - 0 12ld ~-/~z8+) + 0 111ds/z8 + ) 591g7/26+) + 0 2Side-)z6+) + 0 251g)-/t26+ ) - 0 141gT/z8 +) 451d~-/~8 +) - 0 13[g7/26 +) 531g7/28 +) - 0 311d y/~8 +) - 0 2 llg 7/~8 +)

g7/2 band

2+ 21 9+ 21

0 116 0 573

~11+ , ~3+

0 752 1 216

,,+

1 421

T17+ , ~19+ , T

1 779 1 997 2 522

g9/2 b a n d 9+ 23 t,+ 2-3 2

0 871g7/20+) - 0 391gT/t20 +) - 0 231g 7/~22+) + 0 17lg 7/~z2+) - 0 63[g7/22+)+0 591ds/22+) + 0 301gv/tz2+?-0 281d~-/122+)- 0 141d5/24+) +

0 121dy)24+) 0 881gy/22+)-o351gT~22+)-o 241g7/24+)+0 161g~)24 +) 063187/24+)-0601ds/z4+)-0 281g~)24+)-0 271d~)24+)-0 171ds/z6 +) +0 131d,L6+> 0 85[gv/24+)-o321g~24+)+o31]gT/26+)-o191g~)26+)-0 161ds/z6 +) +0 101d5)26+) -0 661gT/z6+)+0 581d5/~6+)+0 311g~26+)-0 271d~/~z6+) -0901gv/z6+)+O341g~/~6+)-O 191g7/28+)+0 131g¢28+) 0 751gv/28+)-0521ds/28+)-0 341g7)28+)+0 23[d5/~28+)

0 909 1 230 1 546 1 937 2 292

0 -0 -0 0 -0

671gff/~20+) - 0 791gq/t22+) + 0 671g9/124+) + 0 821g~-/'24+) + 0 671g9/126+) - 0

'~ ~

1 079 1 832

~~

2 417 2 199

0 0 -0 0 0

901h 1,/20+) + 0 901h , ,/22 + ) + 0 941h, ,/22 +) - 0 92]hH/24 + ) - 0 95[h,,/24+) - 0

~z~-

64[g9/~22+) + 0 46[g9/~24+) + 0 64[g9/~22 +) - 0 491g9726 +) - 0 661gff/124+) - 0

221g9/z2+) + 0 231g9/22+) - 0 231g9/1:6+) + 0 221g9/24 +) - 0 211g~/~8+) + 0

191g9124+)-0 181gg/~z4+)+0 221gg/z4+)-0 171g9/26 +) 201g9/26 + ) + 0

18[g9/20 +) 16199/~22~-) 16{gg/z2 +) 15199/24 +)

h,,/2 b a n d

351h , ,/z2 +) - 0 341h , ,/24 + ) - 0 231h I uz4 + ) + 0 32{ht,/26+) - 0 221h 11~/24+ ) - 0

211h ~,1/20+) 191h~-,~/22+) + 0 13lh, w22~) 221h H~/z4+ ) 201h (t~/z4+ ) 201hH/26+ )

~) The mare components of the calculated wave functions are represented by ]jR, A - 1) and [ j - I R , A + 1), where j ( j - l ) denotes the single-particle orbltal occupied by the pamcle(hole) coupled to the core angular m o m e n t u m R Only the second 2 + core state is denoted by a subindex, 1 e R " = 2 + means the first core state

L G Kostova et al / Shape coexzstence

43

seem to be quite reliable. It is worthwhile mentioning that the polarization factors which i n c o r p o r a t e the effect o f shape changes i n d u c e d by the o d d particle are an i m p o r t a n t ingredient o f this calculation Let us make a short c o m m e n t on the E1 transitions de-exciting the ~ - state (fig 6) There are three 9+ candidates for the final state. The g9/2 hole state is not fed from the 11- level This can be explained with the different deformation o f both states The ~ - state decays to the other two 9+ levels, but the 380 6 keV transition is 40 times more intense than the 489 3 keV one (table 1) This feature is not easy to u n d e r s t a n d from simple arguments based on the calculated mixing amplitudes (table 3), which give no preference for a particular 9+ state. In 121] and 123I, ~+ three-quaslpartlcle isomers have been identified 2 5) By means o f g - f a c t o r measurements the configuration 7r(g9/~ds/2g7/2) could be ascribed to both states 5.7) The de-excitation o f these ~+ states shows a striking difference In 121I, the Isomer decays directly to the ~+ m e m b e r o f the AJ = 1 b a n d built on the g9/~ p r o t o n - h o l e state with the c o r r e s p o n d i n g B ( M 1 ) transition rate a m o u n t i n g to 8 5 x 10 -5 W u In 123I, the isomeric state is also de-excited to a (19+) state with B ( M 1 ) = 2 8 x 10 -5 W u The structure o f this 14+ state and that of the following (~+) and (~+) ones is, however, up to now u n k n o w n In the following, a qualitative explanation for this difference is suggested in the frame o f C Q P C model A s s u m i n g the above three-quaslparticle character o f the ~1+ isomer, the 2 1 + ~ + transition in 121I can be considered as an /-forbidden g7/2~ds/2 transition o f the type 3 Q P ~ I Q P The C Q P C calculations for 121I and 12~I [refs 56)] provide in addition to the states o f the g9/2 b a n d further levels with p r e d o m i n a n t g9/2 structure, but with the angular m o m e n t a J = J m ~ - 3. Between the latter J = - 15+, 17+ and ~9+ states and the 211+, 123+and 1~+ members o f the g9/2 b a n d the model predicts large transition probablhties The theoretical level energies o f these states are in 123I shifted by about 250 keV d o w n to lower energies c o m p a r e d with 121I. On the other hand, the ~1+ isomeric state in 123I is observed at about 300 keV higher excitation energy than in 121I Regarding the 2481 7 keV state in 123I as the ~+ m e m b e r of the g9/2 b a n d and taking Into consideration the model predictions, the transition to the 19+ ~state at 2361 9 keV in 123I appears more probable than the de-excitation to the 19+ ~- state o f the g9/2 b a n d For energetlcai reasons, a ~+ rr(g9)2ds/zg7/2) state in 1-'5I should be shifted to even higher energies and p r o b a b l y therefore has not been observed in our (a, 2n) reaction study

43

EVIDENCE

FOR THREE-QUASIPARTICLE

S T A T E S IN 1251

In f o r m e r Investigations, some three-quasiparticle states which are de-excited by E1 transitions have already been identified in this mass region (cf also subsect 4 2) Thus, in 131Xe [ref 13)] the 19+ state at 1805 7 keV is s u p p o s e d to arise from 2 the u(hll/2d3/2) configuration and decays to the _~ 19- m e m b e r o f the htl/2 collective

44

L G Kostova et al / Shape coexistence

band with B(E1) = 2.8 x 10 -6 W.u In 119Sb, a new ~ - isomer was recently found 14) decaying to the ~+ m e m b e r of the g9/2 rotational band with B(E1) = 6.0 x 10 7 W u For the states at 2350 6, 2586 7 and 2791.0 keV in 125I H a g e m a n n et al 2) tentatively 21 assigned spin values of ~, ~9 and ~, respectively. The panties of these levels which are very probably linked by M1 transitions (cf the conversion electron measurements in ref. 2)) have not been determined and they could not be grouped into collective band structures Their excitation energies and the isomeric character which we found for two of them (fig 6) suggest a three-quasIparticle structure for these states, too The level at 2350.6 keV (T1/2= 1.6 ns) decays by two almost equally intense transitions to the h11/2 and g7/2 rotational bands, respectively (fig 6) Due to the different panties of the final states these AJ = 1 transitions are not of the same multipolarity The data in ref. 2) did not allow the authors to distinguish between E1 or M1 multipolarity for these transiUons Assuming an L = 1 multlpolarlty, we derive for the corresponding absolute transition rates B(E1) ~ 2 . 0 x 10 7W u or B(M1) ~ 2 0 x 10 -5 W.u. for each of the transitions. These values are very low (cf the data on the other known three-quaslpartlcle states given above) and point at a structure of the initial state (2350 6 keV) which is significantly different from that of both final states. Possible interpretations of the states with J = ~7, 19 and ~ can be given on the basis of the couphng of the lowest-lying single-particle states in 125I to the first two-quaslpamcle configurations in the neighbouring even-even nuclei. Twoquaslneutron states of the type ~'(hll/2sl/2)5- and ~'(hll/2d3/2)7- have been observed in the even isotopes of Sn [ref 15)], Te [ref 16)] and Xe [refs 17.18)]. In 124Te (core nucleus for 125I), these states lie at 2334.6 (5-) and 2673.6 keV (7-), respectively 16) I f the description of 125I is restricted to the space consisting of these two-quaslneutron states as well as of the d5/2 and g7/2 proton orbitals (ground and first excited state), the ~ level could arise only from the 7 r g 7 / ~ ' ( h l l / 2 d 3 / 2 ) 7 configuration. For the 19 state two configurations are possible The first one, describing it as another m e m b e r of the ~ - g 7 / ~ ' ( h l l / 2 d 3 / x ) 7 - multlplet can be ruled out. The 204.3 keV ~ 9 transition would be then of intramultiplet type, but the measured transition probability B(M1) = 7 9 x 10 3 W u appears low for such an interpretation. Therefore, we propose the configuration ffds/2L,(hll/2d3/2)7- for the ~9 level The 204.3 keV (M1) isomeric transition linking the ~ and ~ levels would then be o f / - f o r b i d d e n type 7rg7/2~ds/2. The value of the corresponding absolute transition rate B(M1, ~ 9 ) = 7 9 x 10-3 W.u is indeed close to that of the 113 6 k e V 7 r g T / 2 ~ d s / 2 ground-state transition (B(M1, 27+ ~ 2 5+) = 1 5 x 1 0 - 2 W u , r e f 19)) Three candidates to form a state could arise from the set of configurations chosen above One of them ['rrg7/2~,(hll/2d3/2)7- ] s e e m s to be unlikely due to the non-observation of a z~ ~ E2 (mtramultiplet) transition From the other two configurations ~-d5/2 ~'(hl 1/2d3/2)7 and 7"rg7/2~'(hll/2Sl/2) 5- the second one is energetically favoured However, the (M1) 19 17 t r a n s i t i o n 77"d5/2t.,(h11/2d3/2)7-(~)~Trg7/et.,(hll/2S1/2)5-(~) IS expected to appear retarded due to change of orbitals of two particles. The experimental observation 19....~ 17 transition with B(M1,236.1 keV) > 8 3 x 10 -3 W.u for the corresponding ~---,~ seems to contradict this expectation excluding a pure 7rg7/2z,(h~l/2s~/2)5 s t r u c t u r e

L G Kostova et a l / Shape coexistence

45

of the ~ level. We consider therefore a mixture of both 3QP configurations 7rds/2v(h~ 1/2d3/2)7 - and 7rg7/2~'(h 11/2Sl/2)5 as appropriate to explain the experimental data associated with the ~ level In this way, we suggest the following 3QP configurations for the experimentally observed levels under discussion" 7rg7/2~'(hll/zd3/2) 7 for the T2 1 - state, .a'ds/2v(hll/2d3/.,)7- for the ~ state and [TrgT/2U(h~ ~/2s~/2)5- + 7rds/2v(hl 1/2d3/2)7 -] for the ~ - state.

5. Summary and conclusions Applying the generalized centroid-shtft method the half-lives of the levels at 302 2, 641 3,943.5 and 2000 7 keV m 123I as well as at 935 8, 2350.6 and 2791.0 keV in 125I have been measured for the first time Level energies and electromagnetic transitton probabilities in ~25I have been calculated in the frame of the CQPC model. Very good agreement with the experiment is observed lncludmg the half-lives of the 9+ intruder states The different decay patterns of the ~+ isomers In ~21I and 123I are also discussed within this model The states at 2350.6, 2586 7 and 2791 0 keV in 125I are suggested to have a three-quastparticle character The authors from Sofia are mdebted to the Committee for Science, Bulgaria for the financial support under contract No258

References 1) K Heyde, P Van Isacker, M Waroqmer, J L Wood and R A Meyer, Phys Reports 102 (1983) 291 2) U Hagemann, H-J Keller and H - F Brmckmann, Nucl Pbys A289 (1977)292 3) W F Plel, Jr, P Chowdury, U Garg, M A Quader, P M Stwertka, S Vajda and D B Fossan, Phys Rev C31 (1985) 456 4) R E Shroy, D M Gordon, M Gal, D B Fossan and A K Gatgalas, Phys Rev C26 (1982)1089, M Gal, D M Gordon, R E Shroy, D B Fossan and A K Galgalas, Phys Rev C26 (1982) 1101 5) U Hagemann, L Kaubler, H-J Keller, F R May, H Prade and F Stary, Nucl Phys A389 (1982) 341 6) F Donau and U Hagemann, Z Phys A293 11979) 31 7) L Kaubler, H Prade, W Enghardt, H -J Keller and F Stary, Book of Abstracts of the sixth Int Conf on hyperfine Interactions, Gronmgen, The Netherlands, 1983, p NP14 8) L G Kostova, W Andrejtscheff, L K Kostov, P Petkov, H Prade, H Rotter, L Kaubler and F Stary, Annual Report 1985, ZfK Rossendorf, ZfK-584 (1986) 23 9) W Andrejtscheff, F Dubbers, P Manfrass and K D Schdhng, Nucl Phys AIg0 (1972) 489, K D Schllhng, L Kaubler, F Stary and W Andrejtscheff, Nucl Phys A265 (1976) 58, W Andrejtscheff et al, Nucleomka 23 (1978) 159 10) W Andrejtscheff, M Senba, N Tsoupas and Z Z Drag, Nucl instr Meth 204 (1983) 123 11) Tables of Isotopes, ed C M Lederer and V S Shirley (Wdey, New York, 1978) 12) D Janssen, RV Jolos and F Donau, Nucl Phys A224 (1974) 93 13) A Kerek, A Luukko, M Grecescu and J Sztarkler, Nucl Phys A172 (1971) 603 14) M Ionescu-Bujor, A lordanescu, G Pascovlcbl and G Stan-Sion, Annual Report, Dep of Heavy Ion Physics, Bucarest 1984-86 (1987) 34 15) A van Poelgeest, J Bron, W H A Hessehnk, K Allaart, J J A Zalmstra, M J Ultzlnger and H Verheul, Nucl Phys A346 (1980) 70 16) A Kerek, Nucl Phys A176 (1971)466 17) J Hattula, H Helpl and A Luukko, Phys Scnpta 26 (1982) 205 18) H Kusakarl, K Kltao, K Sato, M Sugawara and H Katsugarawa, Nucl Phys A40! (1983) 445 19) PM Endt, At Data Nucl Data Tables 26 (1981) 47